242 Problems El Sdutio~ on Thermcdynam'cs El Statistical Mechanics
Solution:
of photons in the interval dadn:
Considering black body radiation in a cavity we get the number density
The number of photons in the laser beam flowing through an area A per
unit time is dn' = cAdn, and the output power is W = Edn'.
Introducing E = hc/X and dn = n(dO)2 into the expression, we obtain
where
Therefore
2 n A hc2 dX (do)
A5
w, =
T=--. hc^1
Xk ln($+l)
Using the known quantities, we get
WO = 3.60 x lo-' W , T =^6 x lo9 K.
2074
(a) Show that the number of photons in equilibrium at temperature T
in a cavity of volume V is N = V(kT/ft~)~ times a numerical constant.
(b) Use this result to obtain a qualitative expression for the heat ca-
(UC, Berkeley)
pacity of a photon gas at constant volume.
Solution:
(d) The density of states of the photon gas is given by